UK house prices rose by 7.7% in November year-on-year, taking the average price of a home in the UK to £174,910.
House prices in the three months to November were 2.1% higher than in the previous quarter (June-August), below the average increases of 2 to 2.1% recorded in each of the previous four months.
Meanwhile, mortgage approvals for house purchases was 11% higher in the three months to October than in the previous quarter, and 31% higher compared to a year earlier, said the Bank of England.
Housebuilding is picking up too, with private sector housing starts in England up by 10% between the second and third quarters of the year - the highest level since 2008 said the Department for Communities and Local Government.
While the number of home sales also increased, for the sixth month in a row, in October to 94,950, up 24% annually, HMRC announced in its latest report on the property market.
Martin Ellis, Halifax's housing economist, said: "Stronger demand, combined with an insufficient increase in housing supply, has resulted in increases in house prices accompanying higher activity this year.
"Low interest rates, improvements in consumer confidence and official schemes, such as Funding for Lending and Help to Buy, all appear to have boosted demand."
However, he added that the continued squeeze on household budgets - as the rate of inflation outstrips wage growth - is expected to curb house price rises to some extent.
A "revival in housebuilding, which should help bring supply and demand into better balance" would have the same effect, he said.
Nicholas Ayre, managing director of homebuying agency Home Fusion, added: "It is welcome news that figures showing private sector house build starts in England increased by 10% between quarter two and quarter three, to the highest level since 2008, however what we have to bear in mind is the time lag.
"It will take 18-24 months between getting these properties out of the ground and for someone to move in."